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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Ward, A"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2503.09783">arXiv:2503.09783</a> <span> [<a href="https://arxiv.org/pdf/2503.09783">pdf</a>, <a href="https://arxiv.org/format/2503.09783">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Symplectic Geometry">math.SG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> </div> </div> <p class="title is-5 mathjax"> On arborealization, Maslov data, and lack thereof </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Alvarez-Gavela%2C+D">Daniel Alvarez-Gavela</a>, <a href="/search/math?searchtype=author&query=Large%2C+T">Tim Large</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A">Abigail Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2503.09783v1-abstract-short" style="display: inline;"> For a Weinstein manifold, we compare and contrast the properties of admitting an arboreal skeleton and admitting Maslov data. Both properties are implied by the existence of a polarization, for which a basic obstruction is that the odd Chern classes are 2-torsion. In a similar spirit we establish cohomological obstructions to the existence of arboreal skeleta and to the existence of Maslov data, e… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.09783v1-abstract-full').style.display = 'inline'; document.getElementById('2503.09783v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2503.09783v1-abstract-full" style="display: none;"> For a Weinstein manifold, we compare and contrast the properties of admitting an arboreal skeleton and admitting Maslov data. Both properties are implied by the existence of a polarization, for which a basic obstruction is that the odd Chern classes are 2-torsion. In a similar spirit we establish cohomological obstructions to the existence of arboreal skeleta and to the existence of Maslov data, exhibiting concrete examples to illustrate their failure. For instance, we show that complements of smooth anti-canonical divisors in complex projective space may fail to admit either arboreal skeleta or Maslov data. We also exhibit an example of a Weinstein manifold which admits Maslov data but does not admit an arboreal skeleton. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2503.09783v1-abstract-full').style.display = 'none'; document.getElementById('2503.09783v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 March, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2025. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">40 pages, 19 figures; comments welcome</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.03764">arXiv:2408.03764</a> <span> [<a href="https://arxiv.org/pdf/2408.03764">pdf</a>, <a href="https://arxiv.org/ps/2408.03764">ps</a>, <a href="https://arxiv.org/format/2408.03764">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Symplectic Geometry">math.SG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> A universal mirror to $(\mathbb{P}^2, 惟)$ as a birational object </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Keating%2C+A">Ailsa Keating</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A">Abigail Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.03764v1-abstract-short" style="display: inline;"> We study homological mirror symmetry for $(\mathbb{P}^2, 惟)$ viewed as an object of birational geometry, with $惟$ the standard meromorphic volume form. First, we construct universal objects on the two sides of mirror symmetry, focusing on the exact symplectic setting: a smooth complex scheme $U_\mathrm{univ}$ and a Weinstein manifold $M_\mathrm{univ}$, both of infinite type; and we prove homologic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.03764v1-abstract-full').style.display = 'inline'; document.getElementById('2408.03764v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.03764v1-abstract-full" style="display: none;"> We study homological mirror symmetry for $(\mathbb{P}^2, 惟)$ viewed as an object of birational geometry, with $惟$ the standard meromorphic volume form. First, we construct universal objects on the two sides of mirror symmetry, focusing on the exact symplectic setting: a smooth complex scheme $U_\mathrm{univ}$ and a Weinstein manifold $M_\mathrm{univ}$, both of infinite type; and we prove homological mirror symmetry for them. Second, we consider autoequivalences. We prove that automorphisms of $U_\mathrm{univ}$ are given by a natural discrete subgroup of $\operatorname{Bir} (\mathbb{P}^2, \pm 惟)$; and that all of these automorphisms are mirror to symplectomorphisms of $M_\mathrm{univ}$. We conclude with some applications. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.03764v1-abstract-full').style.display = 'none'; document.getElementById('2408.03764v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages, 3 figures; comments welcome</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.02398">arXiv:2401.02398</a> <span> [<a href="https://arxiv.org/pdf/2401.02398">pdf</a>, <a href="https://arxiv.org/format/2401.02398">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> </div> <p class="title is-5 mathjax"> Generating synthetic data for neural operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Hasani%2C+E">Erisa Hasani</a>, <a href="/search/math?searchtype=author&query=Ward%2C+R+A">Rachel A. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.02398v2-abstract-short" style="display: inline;"> Numerous developments in the recent literature show the promising potential of deep learning in obtaining numerical solutions to partial differential equations (PDEs) beyond the reach of current numerical solvers. However, data-driven neural operators all suffer from a similar problem: the data needed to train a network depends on classical numerical solvers such as finite difference or finite ele… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.02398v2-abstract-full').style.display = 'inline'; document.getElementById('2401.02398v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.02398v2-abstract-full" style="display: none;"> Numerous developments in the recent literature show the promising potential of deep learning in obtaining numerical solutions to partial differential equations (PDEs) beyond the reach of current numerical solvers. However, data-driven neural operators all suffer from a similar problem: the data needed to train a network depends on classical numerical solvers such as finite difference or finite element, among others. In this paper, we propose a different approach to generating synthetic functional training data that does not require solving a PDE numerically. We draw a large number $N$ of independent and identically distributed 'random functions' $u_j$ from the underlying solution space (e.g., $H_0^1(惟)$) in which we know the solution lies according to classical theory. We then plug each such random candidate solution into the equation and get a corresponding right-hand side function $f_j$ for the equation, and consider $(f_j, u_j)_{j=1}^N$ as supervised training data for learning the underlying inverse problem $f \rightarrow u$. This `backwards' approach to generating training data only requires derivative computations, in contrast to standard `forward' approaches, which require a numerical PDE solver, enabling us to generate many data points quickly and efficiently. While the idea is simple, we hope this method will expand the potential for developing neural PDE solvers that do not depend on classical numerical solvers. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.02398v2-abstract-full').style.display = 'none'; document.getElementById('2401.02398v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2308.04563">arXiv:2308.04563</a> <span> [<a href="https://arxiv.org/pdf/2308.04563">pdf</a>, <a href="https://arxiv.org/format/2308.04563">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1017/fms.2024.85">10.1017/fms.2024.85 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Periods of elliptic surfaces with $p_g=q=1$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Engel%2C+P">Philip Engel</a>, <a href="/search/math?searchtype=author&query=Greer%2C+F">Fran莽ois Greer</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A">Abigail Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2308.04563v2-abstract-short" style="display: inline;"> We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with 12 nodal fibers, and that its degree is larger than 1. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2308.04563v2-abstract-full" style="display: none;"> We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with 12 nodal fibers, and that its degree is larger than 1. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.04563v2-abstract-full').style.display = 'none'; document.getElementById('2308.04563v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 14J27 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Forum of Mathematics, Sigma 12 (2024) e111 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.11407">arXiv:2106.11407</a> <span> [<a href="https://arxiv.org/pdf/2106.11407">pdf</a>, <a href="https://arxiv.org/ps/2106.11407">ps</a>, <a href="https://arxiv.org/format/2106.11407">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> Asymptotically Optimal Idling in the GI/GI/N+GI Queue </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Zhong%2C+Y">Yueyang Zhong</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a>, <a href="/search/math?searchtype=author&query=Puha%2C+A+L">Amber L. Puha</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2106.11407v2-abstract-short" style="display: inline;"> We formulate a control problem for a GI/GI/N+GI queue, whose objective is to trade off the long-run average operational costs (i.e., abandonment costs and holding costs) with server utilization costs. To solve the control problem, we consider an asymptotic regime in which the arrival rate and the number of servers grow large. The solution to an associated fluid control problem motivates that non-i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.11407v2-abstract-full').style.display = 'inline'; document.getElementById('2106.11407v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.11407v2-abstract-full" style="display: none;"> We formulate a control problem for a GI/GI/N+GI queue, whose objective is to trade off the long-run average operational costs (i.e., abandonment costs and holding costs) with server utilization costs. To solve the control problem, we consider an asymptotic regime in which the arrival rate and the number of servers grow large. The solution to an associated fluid control problem motivates that non-idling service disciplines are not in general optimal, unless some arrivals are turned away. We propose an admission control policy designed to ensure servers have sufficient idle time that we show is asymptotically optimal. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.11407v2-abstract-full').style.display = 'none'; document.getElementById('2106.11407v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2102.04937">arXiv:2102.04937</a> <span> [<a href="https://arxiv.org/pdf/2102.04937">pdf</a>, <a href="https://arxiv.org/ps/2102.04937">ps</a>, <a href="https://arxiv.org/format/2102.04937">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Applications">stat.AP</span> </div> </div> <p class="title is-5 mathjax"> Stationary Distribution Convergence of the Offered Waiting Processes in Heavy Traffic under General Patience Time Scaling </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lee%2C+C">Chihoon Lee</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a>, <a href="/search/math?searchtype=author&query=Ye%2C+H">Heng-Qing Ye</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2102.04937v1-abstract-short" style="display: inline;"> We study a sequence of single server queues with customer abandonment (GI/GI/1+GI) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known ([20, 18]) that the sequence of scaled offered waiting time processes converges weakly to a reflecting diffusion process with non-linear drift, as the traffic intensity approaches… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.04937v1-abstract-full').style.display = 'inline'; document.getElementById('2102.04937v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2102.04937v1-abstract-full" style="display: none;"> We study a sequence of single server queues with customer abandonment (GI/GI/1+GI) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known ([20, 18]) that the sequence of scaled offered waiting time processes converges weakly to a reflecting diffusion process with non-linear drift, as the traffic intensity approaches one. In this paper, we further show that the sequence of stationary distributions and moments of the offered waiting times, with diffusion scaling, converge to those of the limit diffusion process. This justifies the stationary performance of the diffusion limit as a valid approximation for the stationary performance of the GI/GI/1+GI queue. Consequently, we also derive the approximation for the abandonment probability for the GI/GI/1+GI queue in the stationary state. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.04937v1-abstract-full').style.display = 'none'; document.getElementById('2102.04937v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2102.02710">arXiv:2102.02710</a> <span> [<a href="https://arxiv.org/pdf/2102.02710">pdf</a>, <a href="https://arxiv.org/format/2102.02710">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Performance">cs.PF</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> Matching Impatient and Heterogeneous Demand and Supply </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Aveklouris%2C+A">Angelos Aveklouris</a>, <a href="/search/math?searchtype=author&query=DeValve%2C+L">Levi DeValve</a>, <a href="/search/math?searchtype=author&query=Stock%2C+M">Maximiliano Stock</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2102.02710v5-abstract-short" style="display: inline;"> Service platforms must determine rules for matching heterogeneous demand (customers) and supply (workers) that arrive randomly over time and may be lost if forced to wait too long for a match. Our objective is to maximize the cumulative value of matches, minus costs incurred when demand and supply wait. We develop a fluid model, that approximates the evolution of the stochastic model, and captures… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.02710v5-abstract-full').style.display = 'inline'; document.getElementById('2102.02710v5-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2102.02710v5-abstract-full" style="display: none;"> Service platforms must determine rules for matching heterogeneous demand (customers) and supply (workers) that arrive randomly over time and may be lost if forced to wait too long for a match. Our objective is to maximize the cumulative value of matches, minus costs incurred when demand and supply wait. We develop a fluid model, that approximates the evolution of the stochastic model, and captures explicitly the nonlinear dependence between the amount of demand and supply waiting and the distribution of their patience times, also known as reneging or abandonment times in the literature. The fluid model invariant states approximate the steady-state mean queue-lengths in the stochastic system, and, therefore, can be used to develop an optimization problem whose optimal solution provides matching rates between demand and supply types that are asymptotically optimal (on fluid scale, as demand and supply rates grow large). We propose a discrete review matching policy that asymptotically achieves the optimal matching rates. We further show that when the aforementioned matching optimization problem has an optimal extreme point solution, which occurs when the patience time distributions have increasing hazard rate functions, a state-independent priority policy, that ranks the edges on the bipartite graph connecting demand and supply, is asymptotically optimal. A key insight from this analysis is that the ranking critically depends on the patience time distributions, and may be different for different distributions even if they have the same mean, demonstrating that models assuming, e.g., exponential patience times for tractability, may lack robustness. Finally, we observe that when holding costs are zero, a discrete review policy, that does not require knowledge of inter-arrival and patience time distributions, is asymptotically optimal. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.02710v5-abstract-full').style.display = 'none'; document.getElementById('2102.02710v5-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2101.11546">arXiv:2101.11546</a> <span> [<a href="https://arxiv.org/pdf/2101.11546">pdf</a>, <a href="https://arxiv.org/ps/2101.11546">ps</a>, <a href="https://arxiv.org/format/2101.11546">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Symplectic Geometry">math.SG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Algebraic Geometry">math.AG</span> </div> </div> <p class="title is-5 mathjax"> Homological mirror symmetry for elliptic Hopf surfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Ward%2C+A">Abigail Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2101.11546v1-abstract-short" style="display: inline;"> We show homological mirror symmetry results relating coherent analytic sheaves on some complex elliptic surfaces and objects of certain Fukaya categories. We first define the notion of a non-algebraic Landau-Ginzburg model on $\mathbb{R} \times S^1$ and its associated Fukaya category, and show that non-K盲hler sur-faces obtained by performing two logarithmic transformations to the product of the pr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.11546v1-abstract-full').style.display = 'inline'; document.getElementById('2101.11546v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2101.11546v1-abstract-full" style="display: none;"> We show homological mirror symmetry results relating coherent analytic sheaves on some complex elliptic surfaces and objects of certain Fukaya categories. We first define the notion of a non-algebraic Landau-Ginzburg model on $\mathbb{R} \times S^1$ and its associated Fukaya category, and show that non-K盲hler sur-faces obtained by performing two logarithmic transformations to the product of the projective plane and an elliptic curve have non-algebraic Landau-Ginzburg models as their mirror spaces; this class of surface includes the classical Hopf surface $S^1\times S^3$ and other elliptic primary and secondary Hopf surfaces. We also define localization maps from the Fukaya categories associated to the Landau-Ginzburg models to partially wrapped and fully wrapped categories. We show mirror symmetry results that relate the partially wrapped and fully wrapped categories to spaces of coherent analytic sheaves on open submanifolds of the compact complex surfaces in question, and we use these results to sketch a proof of a full HMS result. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.11546v1-abstract-full').style.display = 'none'; document.getElementById('2101.11546v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">69 pages, 3 figures, comments welcome</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2101.04254">arXiv:2101.04254</a> <span> [<a href="https://arxiv.org/pdf/2101.04254">pdf</a>, <a href="https://arxiv.org/format/2101.04254">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Nonhomogeneous $T(1)$ Theorem on Product Quasimetric Spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Nguyen%2C+T+T+T">Trang T. T. Nguyen</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a>, <a href="/search/math?searchtype=author&query=Wick%2C+B+D">Brett D. Wick</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2101.04254v1-abstract-short" style="display: inline;"> In this paper, we provide a non-homogeneous $T(1)$ theorem on product spaces $(X_1 \times X_2, 蟻_1 \times 蟻_2, 渭_1 \times 渭_2)$ equipped with a quasimetric $蟻_1 \times 蟻_2$ and a Borel measure $渭_1 \times 渭_2$, which, need not be doubling but satisfies an upper control on the size of quasiballs. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2101.04254v1-abstract-full" style="display: none;"> In this paper, we provide a non-homogeneous $T(1)$ theorem on product spaces $(X_1 \times X_2, 蟻_1 \times 蟻_2, 渭_1 \times 渭_2)$ equipped with a quasimetric $蟻_1 \times 蟻_2$ and a Borel measure $渭_1 \times 渭_2$, which, need not be doubling but satisfies an upper control on the size of quasiballs. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.04254v1-abstract-full').style.display = 'none'; document.getElementById('2101.04254v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 42B20; Secondary 30L99; 43A15 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2002.07616">arXiv:2002.07616</a> <span> [<a href="https://arxiv.org/pdf/2002.07616">pdf</a>, <a href="https://arxiv.org/format/2002.07616">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Zygmund type and flag type maximal functions, and sparse operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Flores%2C+G+J">Guillermo J. Flores</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2002.07616v2-abstract-short" style="display: inline;"> We prove that the maximal functions associated with a Zygmund dilation dyadic structure in three-dimensional Euclidean space, and with the flag dyadic structure in two-dimensional Euclidean space, cannot be bounded by multiparameter sparse operators associated with the corresponding dyadic grid. We also obtain supplementary results about the absence of sparse domination for the strong dyadic maxim… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2002.07616v2-abstract-full').style.display = 'inline'; document.getElementById('2002.07616v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2002.07616v2-abstract-full" style="display: none;"> We prove that the maximal functions associated with a Zygmund dilation dyadic structure in three-dimensional Euclidean space, and with the flag dyadic structure in two-dimensional Euclidean space, cannot be bounded by multiparameter sparse operators associated with the corresponding dyadic grid. We also obtain supplementary results about the absence of sparse domination for the strong dyadic maximal function. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2002.07616v2-abstract-full').style.display = 'none'; document.getElementById('2002.07616v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 March, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 February, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2020. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2001.04630">arXiv:2001.04630</a> <span> [<a href="https://arxiv.org/pdf/2001.04630">pdf</a>, <a href="https://arxiv.org/ps/2001.04630">ps</a>, <a href="https://arxiv.org/format/2001.04630">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s12220-021-00714-0">10.1007/s12220-021-00714-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Functions of bounded mean oscillation and quasisymmetric mappings on spaces of homogeneous type </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Nguyen%2C+T+T+T">Trang T. T. Nguyen</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2001.04630v2-abstract-short" style="display: inline;"> We establish a connection between the function space BMO and the theory of quasisymmetric mappings on \emph{spaces of homogeneous type} $\widetilde{X} :=(X,蟻,渭)$. The connection is that the logarithm of the generalised Jacobian of an $畏$-quasisymmetric mapping $f: \widetilde{X} \rightarrow \widetilde{X}$ is always in $\rm{BMO}(\widetilde{X})$. In the course of proving this result, we first show th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.04630v2-abstract-full').style.display = 'inline'; document.getElementById('2001.04630v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2001.04630v2-abstract-full" style="display: none;"> We establish a connection between the function space BMO and the theory of quasisymmetric mappings on \emph{spaces of homogeneous type} $\widetilde{X} :=(X,蟻,渭)$. The connection is that the logarithm of the generalised Jacobian of an $畏$-quasisymmetric mapping $f: \widetilde{X} \rightarrow \widetilde{X}$ is always in $\rm{BMO}(\widetilde{X})$. In the course of proving this result, we first show that on $\widetilde{X}$, the logarithm of a reverse-H枚lder weight $w$ is in $\rm{BMO}(\widetilde{X})$, and that the above-mentioned connection holds on metric measure spaces $\widehat{X} :=(X,d,渭)$. Furthermore, we construct a large class of spaces $(X,蟻,渭)$ to which our results apply. Among the key ingredients of the proofs are suitable generalisations to $(X,蟻,渭)$ from the Euclidean or metric measure space settings of the Calder贸n--Zygmund decomposition, the Vitali Covering Theorem, the Radon--Nikodym Theorem, a lemma which controls the distortion of sets under an $畏$-quasisymmetric mapping, and a result of Heinonen and Koskela which shows that the volume derivative of an $畏$-quasisymmetric mapping is a reverse-H枚lder weight. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.04630v2-abstract-full').style.display = 'none'; document.getElementById('2001.04630v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 42B35 (Primary) 30L10; 42B25; 30C65; 46B22; 28C15; 28A20 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1810.03788">arXiv:1810.03788</a> <span> [<a href="https://arxiv.org/pdf/1810.03788">pdf</a>, <a href="https://arxiv.org/ps/1810.03788">ps</a>, <a href="https://arxiv.org/format/1810.03788">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Atomic decomposition of product Hardy spaces via wavelet bases on spaces of homogeneous type </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Han%2C+Y">Yongsheng Han</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Pereyra%2C+M+C">M. Cristina Pereyra</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1810.03788v2-abstract-short" style="display: inline;"> We provide an atomic decomposition of the product Hardy spaces $H^p(\widetilde{X})$ which were recently developed by Han, Li, and Ward in the setting of product spaces of homogeneous type $\widetilde{X} = X_1 \times X_2$. Here each factor $(X_i,d_i,渭_i)$, for $i = 1$, $2$, is a space of homogeneous type in the sense of Coifman and Weiss. These Hardy spaces make use of the orthogonal wavelet base… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1810.03788v2-abstract-full').style.display = 'inline'; document.getElementById('1810.03788v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1810.03788v2-abstract-full" style="display: none;"> We provide an atomic decomposition of the product Hardy spaces $H^p(\widetilde{X})$ which were recently developed by Han, Li, and Ward in the setting of product spaces of homogeneous type $\widetilde{X} = X_1 \times X_2$. Here each factor $(X_i,d_i,渭_i)$, for $i = 1$, $2$, is a space of homogeneous type in the sense of Coifman and Weiss. These Hardy spaces make use of the orthogonal wavelet bases of Auscher and Hyt枚nen and their underlying reference dyadic grids. However, no additional assumptions on the quasi-metric or on the doubling measure for each factor space are made. To carry out this program, we introduce product $(p,q)$-atoms on $\widetilde{X}$ and product atomic Hardy spaces $H^{p,q}_{\rm at}(\widetilde{X})$. As consequences of the atomic decomposition of $H^p(\widetilde{X})$, we show that for all $q > 1$ the product atomic Hardy spaces coincide with the product Hardy spaces, and we show that the product Hardy spaces are independent of the particular choices of both the wavelet bases and the reference dyadic grids. Likewise, the product Carleson measure spaces ${\rm CMO}^p(\widetilde{X})$, the bounded mean oscillation space ${\rm BMO}(\widetilde{X})$, and the vanishing mean oscillation space ${\rm VMO}(\widetilde{X})$, as defined by Han, Li, and Ward, are also independent of the particular choices of both wavelets and reference dyadic grids. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1810.03788v2-abstract-full').style.display = 'none'; document.getElementById('1810.03788v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 October, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 October, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Minor typos corrected, reference added. Submitted</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 42B35 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1807.00960">arXiv:1807.00960</a> <span> [<a href="https://arxiv.org/pdf/1807.00960">pdf</a>, <a href="https://arxiv.org/ps/1807.00960">ps</a>, <a href="https://arxiv.org/format/1807.00960">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> Weak-type endpoint bounds for Bochner-Riesz means for the Hermite operator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Chen%2C+P">Peng Chen</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a>, <a href="/search/math?searchtype=author&query=Yan%2C+L">Lixin Yan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1807.00960v2-abstract-short" style="display: inline;"> We obtain weak-type $(p, p)$ endpoint bounds for Bochner-Riesz means for the Hermite operator $H=-螖+|x|^2$ in ${\mathbb R}^n, n\geq 2$ and for other related operators for $1\leq p\leq 2n/(n+2)$, extending earlier results of Thangavelu and of Karadzhov. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1807.00960v2-abstract-full" style="display: none;"> We obtain weak-type $(p, p)$ endpoint bounds for Bochner-Riesz means for the Hermite operator $H=-螖+|x|^2$ in ${\mathbb R}^n, n\geq 2$ and for other related operators for $1\leq p\leq 2n/(n+2)$, extending earlier results of Thangavelu and of Karadzhov. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.00960v2-abstract-full').style.display = 'none'; document.getElementById('1807.00960v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 August, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 July, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 42B15; 42B08; 42C10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1711.02148">arXiv:1711.02148</a> <span> [<a href="https://arxiv.org/pdf/1711.02148">pdf</a>, <a href="https://arxiv.org/ps/1711.02148">ps</a>, <a href="https://arxiv.org/format/1711.02148">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> Conditioned Functional Limits and Applications to Queues </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Honnappa%2C+H">Harsha Honnappa</a>, <a href="/search/math?searchtype=author&query=Jain%2C+R">Rahul Jain</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1711.02148v1-abstract-short" style="display: inline;"> We consider a renewal process that is conditioned on the number of events in a fixed time horizon. We prove that a centered and scaled version of this process converges to a Brownian bridge, as the number of events grows large, which relies on first establishing a functional strong law of large numbers result to determine the centering. These results are consistent with the asymptotic behavior of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1711.02148v1-abstract-full').style.display = 'inline'; document.getElementById('1711.02148v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1711.02148v1-abstract-full" style="display: none;"> We consider a renewal process that is conditioned on the number of events in a fixed time horizon. We prove that a centered and scaled version of this process converges to a Brownian bridge, as the number of events grows large, which relies on first establishing a functional strong law of large numbers result to determine the centering. These results are consistent with the asymptotic behavior of a conditioned Poisson process. We prove the limit theorems over triangular arrays of exchangeable random variables, obtained by conditionning a sequence of independent and identically distributed renewal processes. We construct martingale difference sequences with respect to these triangular arrays, and use martingale convergence results in our proofs. To illustrate how these results apply to performance analysis in queueing, we prove that the workload process of a single server queue with conditioned renewal arrival process can be approximated by a reflected diffusion having the sum of a Brownian Bridge and Brownian motion as input to its regulator mapping. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1711.02148v1-abstract-full').style.display = 'none'; document.getElementById('1711.02148v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 November, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Submitted to Advances in/ Journal of Applied Probability</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1709.01701">arXiv:1709.01701</a> <span> [<a href="https://arxiv.org/pdf/1709.01701">pdf</a>, <a href="https://arxiv.org/ps/1709.01701">ps</a>, <a href="https://arxiv.org/format/1709.01701">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Characterization of compactness of commutators of bilinear singular integral operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Chaffee%2C+L">Lucas Chaffee</a>, <a href="/search/math?searchtype=author&query=Chen%2C+P">Peng Chen</a>, <a href="/search/math?searchtype=author&query=Han%2C+Y">Yanchang Han</a>, <a href="/search/math?searchtype=author&query=Torres%2C+R">Rodolfo Torres</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1709.01701v1-abstract-short" style="display: inline;"> The commutators of bilinear Calder贸n-Zygmund operators and point-wise multiplication with a symbol in $cmo$ are bilinear compact operators on product of Lebesgue spaces. This work shows that, for certain non-degenerate Calder贸n-Zygmund operators, the symbol being in $cmo$ is not only sufficient but actually necessary for the compactness of the commutators. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1709.01701v1-abstract-full" style="display: none;"> The commutators of bilinear Calder贸n-Zygmund operators and point-wise multiplication with a symbol in $cmo$ are bilinear compact operators on product of Lebesgue spaces. This work shows that, for certain non-degenerate Calder贸n-Zygmund operators, the symbol being in $cmo$ is not only sufficient but actually necessary for the compactness of the commutators. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1709.01701v1-abstract-full').style.display = 'none'; document.getElementById('1709.01701v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 September, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 42B20; 47B07; 42B35 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1709.00703">arXiv:1709.00703</a> <span> [<a href="https://arxiv.org/pdf/1709.00703">pdf</a>, <a href="https://arxiv.org/ps/1709.00703">ps</a>, <a href="https://arxiv.org/format/1709.00703">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.4064/sm180715-13-12">10.4064/sm180715-13-12 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Cauchy integral, bounded and compact commutators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Nguyen%2C+T+T+T">Trang T. T. Nguyen</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a>, <a href="/search/math?searchtype=author&query=Wick%2C+B+D">Brett D. Wick</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1709.00703v2-abstract-short" style="display: inline;"> We study the commutator of the well-known Cauchy integral operator with a locally integrable function $b$ on $\mathbb R$, and establish the characterisation of the BMO space on $\mathbb R$ via the $L^p$ boundedness of this commutator. Moreover, we also establish the characterisation of the VMO space on $\mathbb R$ via the compactness of this commutator. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1709.00703v2-abstract-full" style="display: none;"> We study the commutator of the well-known Cauchy integral operator with a locally integrable function $b$ on $\mathbb R$, and establish the characterisation of the BMO space on $\mathbb R$ via the $L^p$ boundedness of this commutator. Moreover, we also establish the characterisation of the VMO space on $\mathbb R$ via the compactness of this commutator. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1709.00703v2-abstract-full').style.display = 'none'; document.getElementById('1709.00703v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 February, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 September, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">29 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1608.07376">arXiv:1608.07376</a> <span> [<a href="https://arxiv.org/pdf/1608.07376">pdf</a>, <a href="https://arxiv.org/ps/1608.07376">ps</a>, <a href="https://arxiv.org/format/1608.07376">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On weak-star convergence in product Hardy spaces on spaces of homogeneous type </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lee%2C+M">Ming-Yi Lee</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1608.07376v1-abstract-short" style="display: inline;"> A classical theorem of Jones and Journ茅 on weak-star convergence in the Hardy space $H^1$ was generalised to the multiparameter setting by Pipher and Treil. We prove the analogous result when the underlying space is a product space of homogeneous type. The main tools we use for this setting are from recent work in papers by Chen, Li and Ward and by Han, Li and Ward. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1608.07376v1-abstract-full" style="display: none;"> A classical theorem of Jones and Journ茅 on weak-star convergence in the Hardy space $H^1$ was generalised to the multiparameter setting by Pipher and Treil. We prove the analogous result when the underlying space is a product space of homogeneous type. The main tools we use for this setting are from recent work in papers by Chen, Li and Ward and by Han, Li and Ward. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1608.07376v1-abstract-full').style.display = 'none'; document.getElementById('1608.07376v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 August, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 42B30; 42B35; 30L99 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1512.01607">arXiv:1512.01607</a> <span> [<a href="https://arxiv.org/pdf/1512.01607">pdf</a>, <a href="https://arxiv.org/ps/1512.01607">ps</a>, <a href="https://arxiv.org/format/1512.01607">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> Marcinkiewicz-type spectral multipliers on Hardy and Lebesgue spaces on product spaces of homogeneous type </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Chen%2C+P">Peng Chen</a>, <a href="/search/math?searchtype=author&query=Duong%2C+X+T">Xuan Thinh Duong</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a>, <a href="/search/math?searchtype=author&query=Yan%2C+L">Lixin Yan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1512.01607v1-abstract-short" style="display: inline;"> Let $X_1$ and $X_2$ be metric spaces equipped with doubling measures and let $L_1$ and $L_2$ be nonnegative self-adjoint second-order operators acting on $L^2(X_1)$ and $L^2(X_2)$ respectively. We study multivariable spectral multipliers $F(L_1, L_2)$ acting on the Cartesian product of $X_1$ and $X_2$. Under the assumptions of the finite propagation speed property and Plancherel or Stein--Tomas re… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1512.01607v1-abstract-full').style.display = 'inline'; document.getElementById('1512.01607v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1512.01607v1-abstract-full" style="display: none;"> Let $X_1$ and $X_2$ be metric spaces equipped with doubling measures and let $L_1$ and $L_2$ be nonnegative self-adjoint second-order operators acting on $L^2(X_1)$ and $L^2(X_2)$ respectively. We study multivariable spectral multipliers $F(L_1, L_2)$ acting on the Cartesian product of $X_1$ and $X_2$. Under the assumptions of the finite propagation speed property and Plancherel or Stein--Tomas restriction type estimates on the operators $L_1$ and~$L_2$, we show that if a function~$F$ satisfies a Marcinkiewicz-type differential condition then the spectral multiplier operator $F(L_1, L_2)$ is bounded from appropriate Hardy spaces to Lebesgue spaces on the product space $X_1\times X_2$. We apply our results to the analysis of second-order elliptic operators in the product setting, specifically Riesz-transform-like operators and double Bochner--Riesz means. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1512.01607v1-abstract-full').style.display = 'none'; document.getElementById('1512.01607v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 December, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2015. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1510.07606">arXiv:1510.07606</a> <span> [<a href="https://arxiv.org/pdf/1510.07606">pdf</a>, <a href="https://arxiv.org/ps/1510.07606">ps</a>, <a href="https://arxiv.org/format/1510.07606">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2140/pjm.2017.290.273">10.2140/pjm.2017.290.273 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Differential Harnack Estimates for Fisher's Equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Cao%2C+X">Xiaodong Cao</a>, <a href="/search/math?searchtype=author&query=Liu%2C+B">Bowei Liu</a>, <a href="/search/math?searchtype=author&query=Pendleton%2C+I">Ian Pendleton</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A">Abigail Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1510.07606v2-abstract-short" style="display: inline;"> In this paper, we derive several differential Harnack estimates (also known as Li-Yau-Hamilton-type estimates) for positive solutions of Fisher's equation. We use the estimates to obtain lower bounds on the speed of traveling wave solutions and to construct classical Harnack inequalities. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1510.07606v2-abstract-full" style="display: none;"> In this paper, we derive several differential Harnack estimates (also known as Li-Yau-Hamilton-type estimates) for positive solutions of Fisher's equation. We use the estimates to obtain lower bounds on the speed of traveling wave solutions and to construct classical Harnack inequalities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.07606v2-abstract-full').style.display = 'none'; document.getElementById('1510.07606v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 October, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Pacific J. Math. 290 (2017) 273-300 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1510.02559">arXiv:1510.02559</a> <span> [<a href="https://arxiv.org/pdf/1510.02559">pdf</a>, <a href="https://arxiv.org/ps/1510.02559">ps</a>, <a href="https://arxiv.org/format/1510.02559">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Chen%2C+P">Peng Chen</a>, <a href="/search/math?searchtype=author&query=Duong%2C+X+T">Xuan Thinh Duong</a>, <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a>, <a href="/search/math?searchtype=author&query=Yan%2C+L">Lixin Yan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1510.02559v1-abstract-short" style="display: inline;"> The aim of this article is to develop the theory of product Hardy spaces associated with operators which possess the weak assumption of Davies--Gaffney heat kernel estimates, in the setting of spaces of homogeneous type. We also establish a Calder贸n--Zygmund decomposition on product spaces, which is of independent interest, and use it to study the interpolation of these product Hardy spaces. We th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.02559v1-abstract-full').style.display = 'inline'; document.getElementById('1510.02559v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1510.02559v1-abstract-full" style="display: none;"> The aim of this article is to develop the theory of product Hardy spaces associated with operators which possess the weak assumption of Davies--Gaffney heat kernel estimates, in the setting of spaces of homogeneous type. We also establish a Calder贸n--Zygmund decomposition on product spaces, which is of independent interest, and use it to study the interpolation of these product Hardy spaces. We then show that under the assumption of generalized Gaussian estimates, the product Hardy spaces coincide with the Lebesgue spaces, for an appropriate range of~$p$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.02559v1-abstract-full').style.display = 'none'; document.getElementById('1510.02559v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 October, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted by Math. Z</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1505.05931">arXiv:1505.05931</a> <span> [<a href="https://arxiv.org/pdf/1505.05931">pdf</a>, <a href="https://arxiv.org/format/1505.05931">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Spectral Theory">math.SP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2140/involve.2016.9.517">10.2140/involve.2016.9.517 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Gong%2C+F">Feixue Gong</a>, <a href="/search/math?searchtype=author&query=Meyerson%2C+O">Olivia Meyerson</a>, <a href="/search/math?searchtype=author&query=Meza%2C+J">Jeremy Meza</a>, <a href="/search/math?searchtype=author&query=Stoiciu%2C+M">Mihai Stoiciu</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A">Abigail Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1505.05931v1-abstract-short" style="display: inline;"> We study the $蔚$-pseudospectra $蟽_蔚(A)$ of square matrices $A \in \mathbb{C}^{N \times N}$. We give a complete characterization of the $蔚$-pseudospectrum of any $2 \times 2$ matrix and describe the asymptotic behavior (as $蔚\to 0$) of $蟽_蔚(A)$ for any square matrix $A$. We also present explicit upper and lower bounds for the $蔚$-pseudospectra of bidiagonal matrices, as well as for finite rank oper… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.05931v1-abstract-full').style.display = 'inline'; document.getElementById('1505.05931v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1505.05931v1-abstract-full" style="display: none;"> We study the $蔚$-pseudospectra $蟽_蔚(A)$ of square matrices $A \in \mathbb{C}^{N \times N}$. We give a complete characterization of the $蔚$-pseudospectrum of any $2 \times 2$ matrix and describe the asymptotic behavior (as $蔚\to 0$) of $蟽_蔚(A)$ for any square matrix $A$. We also present explicit upper and lower bounds for the $蔚$-pseudospectra of bidiagonal matrices, as well as for finite rank operators. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.05931v1-abstract-full').style.display = 'none'; document.getElementById('1505.05931v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 May, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 15A18; 47A10; 65F15; 15A60 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Involve 9 (2016) 517-540 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1505.04470">arXiv:1505.04470</a> <span> [<a href="https://arxiv.org/pdf/1505.04470">pdf</a>, <a href="https://arxiv.org/ps/1505.04470">ps</a>, <a href="https://arxiv.org/format/1505.04470">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> On the Control of Fork-Join Networks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=%C3%96zkan%2C+E">Erhun 脰zkan</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1505.04470v2-abstract-short" style="display: inline;"> Networks in which the processing of jobs occurs both sequentially and in parallel are prevalent in many application domains, such as computer systems, healthcare, manufacturing, and project management. The parallel processing of jobs gives rise to synchronization constraints that can be a main reason for job delay. In comparison with feedforward queueing networks that have only sequential processi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.04470v2-abstract-full').style.display = 'inline'; document.getElementById('1505.04470v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1505.04470v2-abstract-full" style="display: none;"> Networks in which the processing of jobs occurs both sequentially and in parallel are prevalent in many application domains, such as computer systems, healthcare, manufacturing, and project management. The parallel processing of jobs gives rise to synchronization constraints that can be a main reason for job delay. In comparison with feedforward queueing networks that have only sequential processing of jobs, the approximation and control of networks that have synchronization constraints is less understood. One well-known modeling framework in which synchronization constraints are prominent is the fork-join processing network. Our objective is to find scheduling rules for fork-join processing networks with multiple job types in which there is first a fork operation, then activities that can be performed in parallel, and then a join operation. The difficulty is that some of the activities that can be performed in parallel require a shared resource. We solve the scheduling problem for that shared server (that is, which type of job to prioritize each time the server becomes available) when that server is in heavy traffic and prove an asymptotic optimality result. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.04470v2-abstract-full').style.display = 'none'; document.getElementById('1505.04470v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 June, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 May, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2015. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1504.00706">arXiv:1504.00706</a> <span> [<a href="https://arxiv.org/pdf/1504.00706">pdf</a>, <a href="https://arxiv.org/ps/1504.00706">ps</a>, <a href="https://arxiv.org/format/1504.00706">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> </div> </div> <p class="title is-5 mathjax"> Stationary Distribution Convergence of the Offered Waiting Processes for GI/GI/1+GI Queues in Heavy Traffic </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Lee%2C+C">Chihoon Lee</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a>, <a href="/search/math?searchtype=author&query=Ye%2C+H">Heng-Qing Ye</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1504.00706v3-abstract-short" style="display: inline;"> A result of Ward and Glynn (2005) asserts that the sequence of scaled offered waiting time processes of the $GI/GI/1+GI$ queue converges weakly to a reflected Ornstein-Uhlenbeck process (ROU) in the positive real line, as the traffic intensity approaches one. As a consequence, the stationary distribution of a ROU process, which is a truncated normal, should approximate the scaled stationary distri… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1504.00706v3-abstract-full').style.display = 'inline'; document.getElementById('1504.00706v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1504.00706v3-abstract-full" style="display: none;"> A result of Ward and Glynn (2005) asserts that the sequence of scaled offered waiting time processes of the $GI/GI/1+GI$ queue converges weakly to a reflected Ornstein-Uhlenbeck process (ROU) in the positive real line, as the traffic intensity approaches one. As a consequence, the stationary distribution of a ROU process, which is a truncated normal, should approximate the scaled stationary distribution of the offered waiting time in a $GI/GI/1+GI$ queue; however, no such result has been proved. We prove the aforementioned convergence, and the convergence of the moments, in heavy traffic, thus resolving a question left open in Ward and Glynn (2005). In comparison to Kingman's classical result in Kingman (1961) showing that an exponential distribution approximates the scaled stationary offered waiting time distribution in a $GI/GI/1$ queue in heavy traffic, our result confirms that the addition of customer abandonment has a non-trivial effect on the queue stationary behavior. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1504.00706v3-abstract-full').style.display = 'none'; document.getElementById('1504.00706v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 April, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">29 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1412.2321">arXiv:1412.2321</a> <span> [<a href="https://arxiv.org/pdf/1412.2321">pdf</a>, <a href="https://arxiv.org/format/1412.2321">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Performance">cs.PF</span> </div> </div> <p class="title is-5 mathjax"> On Transitory Queueing </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Honnappa%2C+H">Harsha Honnappa</a>, <a href="/search/math?searchtype=author&query=Jain%2C+R">Rahul Jain</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1412.2321v1-abstract-short" style="display: inline;"> We introduce a framework and develop a theory of transitory queueing models. These are models that are not only non-stationary and time-varying but also have other features such as the queueing system operates over finite time, or only a finite population arrives. Such models are relevant in many real-world settings, from queues at post-offces, DMV, concert halls and stadia to out-patient departme… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.2321v1-abstract-full').style.display = 'inline'; document.getElementById('1412.2321v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1412.2321v1-abstract-full" style="display: none;"> We introduce a framework and develop a theory of transitory queueing models. These are models that are not only non-stationary and time-varying but also have other features such as the queueing system operates over finite time, or only a finite population arrives. Such models are relevant in many real-world settings, from queues at post-offces, DMV, concert halls and stadia to out-patient departments at hospitals. We develop fluid and diffusion limits for a large class of transitory queueing models. We then introduce three specific models that fit within this framework, namely, the Delta(i)/GI/1 model, the conditioned G/GI/1 model, and an arrival model of scheduled traffic with epoch uncertainty. We show that asymptotically these models are distributionally equivalent, i.e., they have the same fluid and diffusion limits. We note that our framework provides the first ever way of analyzing the standard G/GI/1 model when we condition on the number of arrivals. In obtaining these results, we provide generalizations and extensions of the Glivenko-Cantelli and Donskers Theorem for empirical processes with triangular arrays. Our analysis uses the population acceleration technique that we introduce and develop. This may be useful in analysis of other non-stationary and non-ergodic queuing models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.2321v1-abstract-full').style.display = 'none'; document.getElementById('1412.2321v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 December, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Under review (and revision), Math. of Operations Research</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1404.2938">arXiv:1404.2938</a> <span> [<a href="https://arxiv.org/pdf/1404.2938">pdf</a>, <a href="https://arxiv.org/format/1404.2938">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Staffing Call Centers with Uncertain Arrival Rates and Co-sourcing </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Kocaga%2C+Y+L">Yasar Levent Kocaga</a>, <a href="/search/math?searchtype=author&query=Armony%2C+M">Mor Armony</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1404.2938v1-abstract-short" style="display: inline;"> In a call center, staffing decisions must be made before the call arrival rate is known with certainty. Then, once the arrival rate becomes known, the call center may be over-staffed, in which case staff are being paid to be idle, or under-staffed, in which case many callers hang-up in the face of long wait times. Firms that have chosen to keep their call center operations in-house can mitigate th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1404.2938v1-abstract-full').style.display = 'inline'; document.getElementById('1404.2938v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1404.2938v1-abstract-full" style="display: none;"> In a call center, staffing decisions must be made before the call arrival rate is known with certainty. Then, once the arrival rate becomes known, the call center may be over-staffed, in which case staff are being paid to be idle, or under-staffed, in which case many callers hang-up in the face of long wait times. Firms that have chosen to keep their call center operations in-house can mitigate this problem by co-sourcing; that is, by sometimes outsourcing calls. Then, the required staffing $N$ depends on how the firm chooses which calls to outsource in real-time, after the arrival rate realizes and the call center operates as a $M/M/N+M$ queue with an outsourcing option. Our objective is to find a joint policy for staffing and call outsourcing that minimizes the long run average cost of this two-stage stochastic program when there is a linear staffing cost per unit time and linear costs associated with abandonments and outsourcing. We propose a policy that uses a square-root safety staffing rule, and outsources calls in accordance with a threshold rule that characterizes when the system is "too crowded". Analytically, we establish that our proposed policy is asymptotically optimal, as the mean arrival rate becomes large, when the level of uncertainty in the arrival rate is of the same order as the inherent system fluctuations in the number of waiting customers for a known arrival rate. Through an extensive numerical study, we establish that our policy is extremely robust. In particular, our policy performs remarkably well over a wide range of parameters, and far beyond where it is proved to be asymptotically optimal. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1404.2938v1-abstract-full').style.display = 'none'; document.getElementById('1404.2938v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 April, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2014. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1402.3606">arXiv:1402.3606</a> <span> [<a href="https://arxiv.org/pdf/1402.3606">pdf</a>, <a href="https://arxiv.org/ps/1402.3606">ps</a>, <a href="https://arxiv.org/format/1402.3606">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computer Science and Game Theory">cs.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optimization and Control">math.OC</span> </div> </div> <p class="title is-5 mathjax"> Routing and Staffing when Servers are Strategic </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Gopalakrishnan%2C+R">Ragavendran Gopalakrishnan</a>, <a href="/search/math?searchtype=author&query=Doroudi%2C+S">Sherwin Doroudi</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a>, <a href="/search/math?searchtype=author&query=Wierman%2C+A">Adam Wierman</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1402.3606v4-abstract-short" style="display: inline;"> Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is, and how the work is divided between th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.3606v4-abstract-full').style.display = 'inline'; document.getElementById('1402.3606v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1402.3606v4-abstract-full" style="display: none;"> Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is, and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by the system's routing and staffing policies. This observation has consequences when modeling service system performance, and our objective is to investigate those consequences. We do this in the context of the M/M/N queue, which is the canonical model for large service systems. First, we present a model for "strategic" servers that choose their service rate in order to maximize a trade-off between an "effort cost", which captures the idea that servers exert more effort when working at a faster rate, and a "value of idleness", which assumes that servers value having idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time. We find that the system must operate in a quality-driven regime, in which servers have idle time, in order for an equilibrium to exist, which implies that the staffing must have a first-order term that strictly exceeds that of the common square-root staffing policy. Then, within the class of policies that admit an equilibrium, we (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. Finally, we end by exploring the question of whether routing policies that are based on the service rate, instead of the server idle time, can improve system performance. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.3606v4-abstract-full').style.display = 'none'; document.getElementById('1402.3606v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 March, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 14 February, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">First submitted for journal publication in 2014; accepted for publication in Operations Research in 2016. Presented in select conferences throughout 2014</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1206.0720">arXiv:1206.0720</a> <span> [<a href="https://arxiv.org/pdf/1206.0720">pdf</a>, <a href="https://arxiv.org/format/1206.0720">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Probability">math.PR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s11134-014-9428-4">10.1007/s11134-014-9428-4 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A queueing model with independent arrivals, and its fluid and diffusion limits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Honnappa%2C+H">Harsha Honnappa</a>, <a href="/search/math?searchtype=author&query=Jain%2C+R">Rahul Jain</a>, <a href="/search/math?searchtype=author&query=Ward%2C+A+R">Amy R. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1206.0720v2-abstract-short" style="display: inline;"> We introduce the 螖(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the inter-arrival times are differences of consecutive ordered statistics. They are served by a single server which provides service according to a general distribution G… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1206.0720v2-abstract-full').style.display = 'inline'; document.getElementById('1206.0720v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1206.0720v2-abstract-full" style="display: none;"> We introduce the 螖(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the inter-arrival times are differences of consecutive ordered statistics. They are served by a single server which provides service according to a general distribution G, with independent service times. The exact model is analytically intractable. Thus, we develop fluid and diffusion limits for the various stochastic processes, and performance metrics. The fluid limit of the queue length is observed to be a reflected process, while the diffusion limit is observed to be a function of a Brownian motion and a Brownian bridge process, and is given by a 'netput' process and a directional derivative of the Skorokhod reflected fluid netput in the direction of a diffusion refinement of the netput process. We also observe what may be interpreted as a transient Little's law. Sample path analysis reveals various operating regimes where the diffusion limit switches between a free diffusion, a reflected diffusion process and the zero process, with possible discontinuities during regime switches. The weak convergence is established in the M1 topology, and it is also shown that this is not possible in the J1 topology. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1206.0720v2-abstract-full').style.display = 'none'; document.getElementById('1206.0720v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 December, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 June, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted, Queueing Systems</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 60K25; 90B15 (Primary) 68M20; 90B22 (Secondary) </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Queueing Systems, 2014,0257-0130 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1204.6559">arXiv:1204.6559</a> <span> [<a href="https://arxiv.org/pdf/1204.6559">pdf</a>, <a href="https://arxiv.org/ps/1204.6559">ps</a>, <a href="https://arxiv.org/format/1204.6559">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Classical Analysis and ODEs">math.CA</span> </div> </div> <p class="title is-5 mathjax"> One-parameter and multiparameter function classes are intersections of finitely many dyadic classes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Li%2C+J">Ji Li</a>, <a href="/search/math?searchtype=author&query=Pipher%2C+J">Jill Pipher</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1204.6559v1-abstract-short" style="display: inline;"> We prove that the class of Muckenhoupt A_p weights coincides with the intersection of finitely many suitable translates of dyadic A_p, in both the one-parameter and multiparameter cases, and that the analogous results hold for the reverse H枚lder class RH_p, for doubling measures, and for the space VMO of functions of vanishing mean oscillation. We extend to the multiparameter (product) space BMO o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.6559v1-abstract-full').style.display = 'inline'; document.getElementById('1204.6559v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1204.6559v1-abstract-full" style="display: none;"> We prove that the class of Muckenhoupt A_p weights coincides with the intersection of finitely many suitable translates of dyadic A_p, in both the one-parameter and multiparameter cases, and that the analogous results hold for the reverse H枚lder class RH_p, for doubling measures, and for the space VMO of functions of vanishing mean oscillation. We extend to the multiparameter (product) space BMO of functions of bounded mean oscillation the corresponding one-parameter BMO result due to T. Mei, by means of the Carleson-measure characterization of multiparameter BMO. Our results hold in both the compact and non-compact cases. In addition, we survey several definitions of VMO and prove their equivalences, in the continuous, dyadic, one-parameter and multiparameter cases. We show that the weighted Hardy space H^1(蠅) is the sum of finitely many suitable translates of dyadic weighted H^1(蠅), and that the weighted maximal function is pointwise comparable to the sum of finitely many dyadic weighted maximal functions for suitable translates of the dyadic grid and for each doubling weight 蠅. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.6559v1-abstract-full').style.display = 'none'; document.getElementById('1204.6559v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 April, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">33 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 42B35; 42B30; 42B25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1204.1635">arXiv:1204.1635</a> <span> [<a href="https://arxiv.org/pdf/1204.1635">pdf</a>, <a href="https://arxiv.org/ps/1204.1635">ps</a>, <a href="https://arxiv.org/format/1204.1635">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> </div> </div> <p class="title is-5 mathjax"> A new class of harmonic measure distribution functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Barton%2C+A">Ariel Barton</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1204.1635v1-abstract-short" style="display: inline;"> Let D be a planar domain containing 0. Let h_D(r) be the harmonic measure at 0 in D of the part of the boundary of D within distance r of 0. The resulting function h_D is called the harmonic measure distribution function of D. In this paper we address the inverse problem by establishing several sets of sufficient conditions on a function f for f to arise as a harmonic measure distribution function… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.1635v1-abstract-full').style.display = 'inline'; document.getElementById('1204.1635v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1204.1635v1-abstract-full" style="display: none;"> Let D be a planar domain containing 0. Let h_D(r) be the harmonic measure at 0 in D of the part of the boundary of D within distance r of 0. The resulting function h_D is called the harmonic measure distribution function of D. In this paper we address the inverse problem by establishing several sets of sufficient conditions on a function f for f to arise as a harmonic measure distribution function. In particular, earlier work of Snipes and Ward shows that for each function f that increases from zero to one, there is a sequence of multiply connected domains X_n such that h_{X_n} converges to f pointwise almost everywhere. We show that if f satisfies our sufficient conditions, then f = h_D, where D is a subsequential limit of bounded simply connected domains that approximate the domains X_n. Further, the limit domain is unique in a class of suitably symmetric domains. Thus f = h_D for a unique symmetric bounded simply connected domain D. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.1635v1-abstract-full').style.display = 'none'; document.getElementById('1204.1635v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 April, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">50 pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 30C85; Secondary 30C20; 31A15; 60J65 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1111.1596">arXiv:1111.1596</a> <span> [<a href="https://arxiv.org/pdf/1111.1596">pdf</a>, <a href="https://arxiv.org/ps/1111.1596">ps</a>, <a href="https://arxiv.org/format/1111.1596">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Social and Information Networks">cs.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Adaptation and Self-Organizing Systems">nlin.AO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Physics and Society">physics.soc-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1063/1.4790836">10.1063/1.4790836 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Multi-Stage Complex Contagions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Melnik%2C+S">Sergey Melnik</a>, <a href="/search/math?searchtype=author&query=Ward%2C+J+A">Jonathan A. Ward</a>, <a href="/search/math?searchtype=author&query=Gleeson%2C+J+P">James P. Gleeson</a>, <a href="/search/math?searchtype=author&query=Porter%2C+M+A">Mason A. Porter</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1111.1596v2-abstract-short" style="display: inline;"> The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investigation of complex contagions can provide crucial insights into social influence and behavior-adoption cascades on networks. In this paper, we introduce a model of a multi-stage complex contagion on networks. Agents at diff… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1111.1596v2-abstract-full').style.display = 'inline'; document.getElementById('1111.1596v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1111.1596v2-abstract-full" style="display: none;"> The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investigation of complex contagions can provide crucial insights into social influence and behavior-adoption cascades on networks. In this paper, we introduce a model of a multi-stage complex contagion on networks. Agents at different stages --- which could, for example, represent differing levels of support for a social movement or differing levels of commitment to a certain product or idea --- exert different amounts of influence on their neighbors. We demonstrate that the presence of even one additional stage introduces novel dynamical behavior, including interplay between multiple cascades, that cannot occur in single-stage contagion models. We find that cascades --- and hence collective action --- can be driven not only by high-stage influencers but also by low-stage influencers. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1111.1596v2-abstract-full').style.display = 'none'; document.getElementById('1111.1596v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 November, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 10 figures. This version is accepted to appear in Chaos</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Chaos 23, 013124 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/9604224">arXiv:math/9604224</a> <span> [<a href="https://arxiv.org/pdf/math/9604224">pdf</a>, <a href="https://arxiv.org/ps/math/9604224">ps</a>, <a href="https://arxiv.org/format/math/9604224">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> </div> </div> <p class="title is-5 mathjax"> Fuchsian Groups, Quasiconformal Groups, and Conical Limit Sets </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Jones%2C+P+W">Peter W. Jones</a>, <a href="/search/math?searchtype=author&query=Ward%2C+L+A">Lesley A. Ward</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/9604224v1-abstract-short" style="display: inline;"> We construct examples showing that the normalized Lebesgue measure of the conical limit set of a uniformly quasiconformal group acting discontinuously on the disc may take any value between zero and one. This is in contrast to the cases of Fuchsian groups acting on the disc, conformal groups acting discontinuously on the ball in dimension three or higher, uniformly quasiconformal groups acting d… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9604224v1-abstract-full').style.display = 'inline'; document.getElementById('math/9604224v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/9604224v1-abstract-full" style="display: none;"> We construct examples showing that the normalized Lebesgue measure of the conical limit set of a uniformly quasiconformal group acting discontinuously on the disc may take any value between zero and one. This is in contrast to the cases of Fuchsian groups acting on the disc, conformal groups acting discontinuously on the ball in dimension three or higher, uniformly quasiconformal groups acting discontinuously on the ball in dimension three or higher, and discrete groups of biholomorphic mappings acting on the ball in several complex dimensions. In these cases the normalized Lebesgue measure is either zero or one. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9604224v1-abstract-full').style.display = 'none'; document.getElementById('math/9604224v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 April, 1996; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 1996. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> MSRI 1996-024 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div 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